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A heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water.
Calculate the rise in the water level if the original depth of water was:
a) 10cm
b) 2cm
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Regarding this problem and its solution in the post by @mananth, I'd like to make two notices.
First notice to (1) is that the solution by @mananth is correct ONLY IF the cylindrical tank
has enough height in order for the displaced water does not flow out of the cylinder.
Otherwise, the rise in the water level will be limited by the height of the cylinder.
The problem says nothing about it, and it is the problem's FAULT.
Second notice is that the solution by @mananth for part 2) is FATALLY INCORRECT.
See my correct solution below.
Solution to part 2
The original volume of the water in the tank is = = 307.87582 cm^3.
The area of the horizontal section of the tank, occupied by the water after placing the solid cube
is = = 89.93791 cm^2.
The final level of the water is then = 3.423204075 cm, or 3.423 cm after rounding.
Thus the rise of the water level is the difference 3.423 - 2 = 1.423 cm.
Solved correctly.
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Again, the solution by @mananth for part 2) is CONCEPTUALLY INCORRECT,
since he/she incorrectly determines the volume of the displaced water,
which is of fundamental importance in this problem.